Iredell-Statesville Schools
Integrated Math I
Core Plus - Course 1 Unit 5 Guide
Exponential Functions
Using this guide:
It is the expectation that all teachers will have their classes complete all items listed in this guide, in the order in which it is presented, and completed in the
labeled time frame. At the teacher’s discretion, additional examples, problems, assignments and assessments may be added to this guide.
In the rare instance in which an investigation has already been covered, the teacher should cover the same topic and remediate or extend the students’ learning
in the same time frame.
We will be seeking feedback on the guide as we progress through the year.
Unit 5 Planning Guide (p. 289B)
Exponential Functions develops student ability to recognize and represent exponential growth and decay patterns, to express those patterns in symbolic
forms, to solve problems that involve exponential change, and to use properties of exponents to write expressions in equivalent forms.
Topics include exponential growth and decay functions, data modeling, growth and decay rates, half-life
and doubling time, compound interest, and properties of exponents.
NC Math I Standards covered in this unit:
Still working on this, but coming soon!
Lesson 1: Modeling Linear Relationships
Launch: Students should start on p. 291, reading the first page and looking at all charts, graphs and data provided. The teacher then should lead a class
discussion of the “Think About the Situation.” Use these questions to formatively assess the needs of your class and make adaptations as needed (You will get
better at this as you become more familiar with this curriculum). This is not a time to teach concepts forgotten, only a time to assess the students’ needs. The
investigations that follow will teach or reteach these concepts. You can explain to students that they should be able to figure out the complete answers when
they complete the lesson.
TEACHER OPTION: The Core Plus program puts Properties of Exponents in Lesson 1 Investigation 5 and Lesson 2 Investigations 4 and 5. It is your choice
whether you want to pull those investigations out and create an Exponents lesson before you begin the Growth and Decay lessons.
Explore: Investigation
Topic Description
Investigation 1: Counting in Tree Graphs
(p. 291)
Students will recognize and understand
CYU p.294
exponential patterns using NEXT=b*NOW
OYO p.307 #2, 4, 17-19, 25 (writing
and y=bx
extension), 30 (extension)
2 days
Students work with exponential functions CYU p.298
that start at other numbers then 1.
OYO p.307 #5-6, 21-22, 26, 31 (extension),
Students will recognize the implications
38 (Review)
of exponential growth.
1 day
(Before the investigation use p. 319 #35,36
as a warm up.)
Share, Summarize and Apply
Time Frame
The whole investigation will need be
completed, except #4.
*Use Pay It Forward video clip on
youtube.com
* Myth Busters Video- Paper Folding
Activity could be used to launch this lesson
(as well as Lesson2)
Investigation 2: Getting Started (p. 295)
The whole investigation will need be
completed
*#3 - students don’t need to do all 4 tables
(pick 1 or 2)
Investigation 3: Compound Interest
(p. 298)
The whole investigation will need be
completed
Students will work with exponential
functions in which the growth rate is a
fraction.
CYU p.301
2-3 days
OYO p.307 #7-8, 23, 33 (Extension)
Compound Interest
*Split up #5 so each group has to explain it
to the whole group
*Supplement with worksheet on
compound interest
Investigation 4: Modeling Data Patterns
(p. 302)
Students will learn to find an exponential
model to fit given data.
The whole investigation will need be
completed
Students will be able to recognize when
to use an exponential model.
STM p. 303
1 day
OYO p.307 #11-12, 24, 26-27
(Supplement with worksheet)
*Discuss correlation coefficient and how to
set up diagnostic
*Split up problems #1 and 2 in
Investigation #4 between the groups and
then have groups share with class
Investigation 5: Properties of Exponents I
(p.304)
Students will discover (rediscover) three
basic exponential laws.
CYU p.306
OYO p.307#13-16, 28, 29
The whole investigation will need be
completed
*Need supplemental lesson on proving
properties of exponents (stress expanding
to prove.)
Suggestion: Split among groups: Product of
powers, Power of a power and Power of a
product
1 day
Assessment
Vocabulary to be used in this assessment: Exponential Growth (increase), Exponential Decay (decrease), Initial Value, Compound Interest, Interest Rate,
Regression, Correlation Coefficient
Lesson 2: Exponential Decay
Launch: Students should start on p. 322, reading the first page and looking at all charts, graphs and data provided. The teacher then should lead a class
discussion of the “Think About the Situation.” Use these questions to formatively assess the needs of your class and make adaptations as needed (You will get
better at this as you become more familiar with this curriculum). This is not a time to teach concepts forgotten, only a time to assess the students’ needs. The
investigations that follow will teach or reteach these concepts. You can explain to students that they should be able to figure out the complete answers when
they complete the lesson.
Explore: Investigation
Topic Description
Substitute Investigation #1 with Paper
Folding/M&M/Rhino Activity
Share, Summarize and Apply
Time Frame
*Students will complete handout for Rhino
Activity
1 Day for activities
.5 of next day for
discussion of Rhino
CYU p. 329
1 Day
*Teacher leads Paper folding activity as a
class discussion.
*Students work in groups to complete
M&M activity.
*An option is for the teacher to bring in
half-life as a discussion point with students
after M&M activity is complete.
Investigation 2: Medicine and
Mathematics (p.326)
The whole investigation will need be
completed.
*Teacher will need to discuss what is halflife is with students. (if not done on
previous day).
The students will extend their
understanding of exponential decay by
looking at tables, graphs, and rules.
Interpretation of fractional exponents
OYO p.338 #4-5, 20
*Teacher will need to clarify medical terms
used in the problems.
Investigation 3: Modeling Decay (p. 330)
The whole investigation will need be
completed.
The student will create exponential
models to fit given data.
STM p. 331
1 Day
OYO p.338 #9, 11, 42
Students will compare models created by
logic to those created with technology.
*Will need 100 coins or 100 of one item
and an area split into two parts
*Can be done as a class.
*Optional if needed for lower students.
Investigation #4: Properties of Exponents
II (p.332)
Students will extend their knowledge of
the properties of exponents.
CYU p.334
1.5 Days
OYO p.338 #12-16
*Use the problems from 1, 3, 7 to develop
quotient and negative properties of
exponents.
*Use 2a, 2b, 4a, 4b, 5, 8a for student depth
of knowledge and discussion.
Investigation 5: Square Roots and Radicals The students will build and use an
(p.335)
understanding of rewriting radicals
expressions.
*Use the problems from 1, 2, 5 to develop
ideas of radicals and rational exponents
Connecting square roots to fractional
*Use 4,6 for student depth of knowledge
exponents.
and discussion
*Supplemental Resources on Quotient Rules
and Negative Exponents
CYU p.337 a-c
1 Day
*Supplemental Resources on radicals and
rational exponents
Assessment Coming Soon!
Vocabulary to be used in this assessment: Half-life, Exponential Decay, Radicals, Rational Exponents, Powers of a Fraction, Quotients of Powers, Negative
Exponents, Now-Next
Lesson 3: Looking Back
Launch: This is a review lesson, so there is not a standard launch.
Explore: Investigation
Topic Description
Share, Summarize and Apply
Time Frame
Looking Back (p. 232)
The students will extend their
understanding of exponential decay by
looking at tables, graphs, and rules.
CYU p.359
1-2 days
This is a review lesson that relates the
previous three lessons.
Complete the parts of this lesson that your
class needs for review.
Interpretation of fractional exponents
OYO p.338 - Use any of the suggested
problems from the Unit 5 Planning Guide (p.
289B) from the previous lessons in this Unit.
The student will create exponential
models to fit given data.
Students will compare models created by
logic to those created with technology.
Students will extend their knowledge of
the properties of exponents.
The students will build and use an
understanding of rewriting radicals
expressions.
Connecting square roots to fractional
exponents.
Assessment: Coming Soon!
Vocabulary to be used in this assessment: Exponential Growth (increase), Exponential Decay (decrease), Initial Value, Compound Interest, Interest Rate,
Regression, Correlation Coefficient, Half-life, Exponential Decay, Radicals, Rational Exponents, Powers of a Fraction, Quotients of Powers, Negative Exponents,
Now-Next